Hydrogen atom electron energy levels

On compression of non-hydrogen atoms the energy levels, which in this case are occupied by electrons, respond in the same way. Apart from level crossings, interelectronic interactions now also lead to an internal transfer of energy and splitting of the magnetic sub-levels, such that a single electron eventually reaches the ionization limit on critical compression. The calculated ionization radii obey the same periodic law as the elements and determine the effective size of atoms in chemical interaction. 

Figure 7.8 shows a single transition. However, it is more informative to express transitions as shown in Figure 7.10. Each horizontal line represents an allowed energy level for the electron in a hydrogen atom. The energy levels are labeled with their principal quantum numbers.

Figure 5.12 shows that, unlike rungs on a ladder, however, the hydrogen atom s energy levels are not evenly spaced. Figure 5.12 also illustrates the four electron transitions that account for visible lines in hydrogen s atomic emission spectrum, shown in Figure 5.8. Electron transitions from higher-energy orbits to the second orbit account for all of hydrogen s visible lines, which form the Balmer series. Other electron transitions have been measured that are not visible, such as the Lyman series (ultraviolet), in which electrons drop into the n = I orbit, and the Paschen series (infrared), in which electrons drop into the n = 3 orbit.

The theoretical results for the hydrogen-like atom may be related to experimentally measured spectra. Observed spectral lines arise from transitions of the atom from one electronic energy level to another. The frequency v of any given spectral line is given by the Planck relation... 

Erwin Schrodinger developed an equation to describe the electron in the hydrogen atom as having both wavelike and particle-like behaviour. Solution of the Schrodinger wave equation by application of the so-called quantum mechanics or wave mechanics shows that electronic energy levels within atoms are quantised that is, only certain specific electronic energy levels are allowed. 

We have used the electronic energy levels for atomic hydrogen to serve as a model for other atoms. In a similar way, we can use the interaction of two hydrogen atoms giving the hydrogen molecule as a model for bonding between other atoms. In its simplest form, we can consider the bond between... 

Fig. 2.3. Electronic energy level diagram for the hydrogen atom.

The special stability of benzene (aromaticity) comes from the six tc electrons in three molecular orbitals made up by the overlap of the six atomic p orbitals on the carbon atoms. The energy levels of these orbitals are arranged so that there is exceptional stability in the molecule (a notional 140 kjmor1 over a molecule with three conjugated double bonds), and the shift of the six identical hydrogen atoms in the NMR spectrum (5h 7.2 p.p.m.) is evidence of a ring current in the delocalized tc system. 

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